Solve the absolute value inequality. |2-5x| < or equal to 0. (2 minus 5x is less than or equal to 0)
| 2 - 5x | <= 0
the absolute value is always positive. Therefore, it is never less than zero. It can, however, be equal to zero:
2 - 5x = 0
x = 2/5
To solve |2-5x| < = 0
If 2-5x is < 0 then |2-5x| = 5x-2 by definition . So 5x-2 < 0 by definition.
It is a contradiction
If 2-5x > 0, then |2-5x| =2-5x by definition. So 2-5x < 0 a contradiction.
So x > 2/5.
2 < 5x, x >2/5.
So x cannot be greater than 2/5 and x cannot be less than 2/5.
Therefore x = 2/5 is the only value that satisfies |2-5x| < = 0.
|2-5x| < or equal to 0
the l l makes the numbers positive so:
2 + 5x < or equal to 0
now move the 5x
2 `<=` -5x
divide by -5
`2/-5 >= x`
now change the sign since you divided:
`2/-5 lt=` `x`
|2-5x| < or equal to 0.
so 2-5x< or equal to 0
Move the 5x on the other side so the equation stays positive
then simply divide by 5 to isolate the variable (x)
The sign changed because you divided by 5, once you divide it changes the sign
So the answer is x>2/5
Thank you so much!